A) \[{{E}_{2}}-{{E}_{1}},\]
B) \[1.1577\times {{10}^{-38}}\]
C) \[2.9\times {{10}^{-35}}\]
D) None of these
Correct Answer: B
Solution :
Let\[I=\int_{{}}^{{}}{\frac{1-{{x}^{2}}}{(1+{{x}^{2}})\sqrt{1+{{x}^{4}}}}dx}\] \[=\int_{{}}^{{}}{\frac{\frac{1}{{{x}^{2}}}-1}{\left( x+\frac{1}{x} \right)\sqrt{{{x}^{2}}+\frac{1}{{{x}^{2}}}}}dx}\] \[=-\int_{{}}^{{}}{\frac{1}{\left( x+\frac{1}{x} \right)\sqrt{{{\left( x+\frac{1}{x} \right)}^{2}}-{{(\sqrt{2})}^{2}}}}d\left( x+\frac{1}{x} \right)}\] \[=\frac{1}{\sqrt{2}}\cos e{{c}^{-1}}\left( \frac{x+\frac{1}{x}}{\sqrt{2}} \right)+C\] \[=\frac{1}{\sqrt{2}}{{\sin }^{-1}}\left( \frac{\sqrt{2}x}{{{x}^{2}}+1} \right)+C\]
You need to login to perform this action.
You will be redirected in
3 sec
